CARDIOVASCULAR INTERACTIONS Carl Rothe and John Gersting The mathematical Model was designed to demonstrate and clarify the interactions between the heart and peripheral circulation in the development and control of an adequate cardiac output and systemic arterial blood pressure. The interactive Tutorial was designed to help your understanding of the physiology of the circulatory system, including the causes-and-effects involved with function. Please Note: A ten-page Descriptive paper and Instructions for downloading the CVI Project, as zipped files, are available at the American Physiological Society web site for Advances in Physiology Education at: http::/advan.physiology.org/cgi/content/full/26/2/98/DC1 Abstract Cardiovascular Interactions is an active learning tool that demonstrates the complex and intricate interactions between the functions of the heart and peripheral circulation. This learning package, for both teachers and students, consists of a Lab Book, a Model, and an Information File. The Lab Book is an interactive tutorial for exploring the relative influences of parameter changes on the cardiovascular system. Consequences of heart failure, hemorrhage, and exercise can also be explored. The results obtained in the Lab Book are based on the Model used. The mathematical Model reflects our current understanding of the basic function of the cardiovascular system. It was designed to be complex enough to be realistic, yet not so complex as to be overwhelming. The Model has five compartments including a left ventricle, systemic arterial bed, venous bed, right ventricle, and a lung bed to represent the major parts of the cardiovascular system. It includes 15 defining parameters and 32 variables. It is based on five basic relationships: 1. Conservation of mass related to the difference between inflow, outflow and the accumulation of stressed volume in a compartment, using differencedifferential equations solved iteratively at 0.001 min intervals; 2. Distending Pressure related to stressed volume and compliance; 3. Flow related to pressure gradient and resistance; 4. Cardiac output as Heart Rate times (End-Diastolic-Volume minus EndSystolic Volume), and 5. Vigor of cardiac contraction related to end-diastolic-volume (Starling’s Law of the Heart) and end-systolic-pressure (Emax). An Information File contains definitions and descriptions of key classical physiology concepts, including figures, and a discussion of the Lab Book “experiments”. A detailed description of the model and documentation of parameter values user are included. An Index and Hypertext tags embedded in the Lab Book provide ready access to the contents of this file. Both the Information and help file and the Lab Book have a detailed Table of Contents. -o-o-o-o-oDesigned to be run from its CD, the Cardiovascular Interactions learning package need not be installed on the user’s computer. The downloaded files can be run from a computer with Microsoft Windows without installation. Learners Targeted This project will improve the understanding of the cardio-vascular system at the total body level for: medical, graduate and bioengineering students and also Professors, Clinicians, and Scientists who need a clear and consistent grasp of its complexities. The project may be used for: 1. Your review of concepts and the approach of chains of logic through causeand-effect 2. Part of a physiology laboratory course with students discussing and learning in groups of 2 or 3. 3. Lecture display of only the Model and Data Plot. 4. Alternative to animal laboratory, with student assigned to specific experiments, predictions expected, questions answered and floppy with Lab Book submitted to Instructor. 5. Distributed (asynchronous) education tool for topics not covered during lecture time. 6. Continuing education for anesthesiologists, cardiovascular surgeons, emergency medicine physicians. 7. Bioengineers needing more physics applied to physiology and an example of a complex mechanical system with negative feedback control. Topics included for helping the Learner: ⇒ Explain the difference between Emax (related to afterload, that is ventricular end systolic pressure) and the Frank-Starling law of the heart (related to preload, that is ventricular end diastolic volume) as major determinants of the vigor of cardiac contraction. ⇒ Explain how a change in each characterizing parameter of the cardiovascular system, such as resistance, compliance, total stressed volume, vigor of cardiac contraction, heart rate, or intrathoracic pressure modifies cardiovascular function. ⇒ Explain why changes in blood volume distribution and vascular capacitance are important parts of the inherent, hydraulic mechanisms for cardiovascular homeostasis. ⇒ Discover which parameter changes are most effective for providing compensation for heart failure, vigorous exercise, or hemorrhage. ⇒ Understand why a venous resistance, which provides a difference between central venous and peripheral venous pressures, is necessary for explaining the coupling between the heart and peripheral vasculature. ⇒ Explain whether Cardiac output controls Right atrial pressure. ⇒ Explain whether Right atrial pressure controls Venous return. ⇒ Explain why the ventricular ejection fraction, while useful, is not a fully adequate measure of cardiac contractility. ⇒ Predict conditions under which venous return does not equal cardiac output and in what direction and why not. Model Characteristics The five-compartment mathematical model is simulated by a series of equations that, in conjunction with the parameters, define the system function and the magnitude of the variables (e.g. outflow, pressure, and distended volume) of each compartment. The two facets of the Vigor of Cardiac contraction, revealed and emphasized with the Model, are: a) The magnitude of preload (the end-diastolic volume that is the basis of the Frank-Starling Law of the Heart), and b) The magnitude of afterload (the end-systolic pressure that, with Emax, determines the end-systolic volume). Implementation of the Conservation of Mass principle is the key to the utility and reliability of the model. Using this principle, volume is redistributed between the five compartments in accordance with the current parameter set used. The Model demonstrates the concept that mechanical feedback mechanisms (such as passive blood volume redistribution influence on ventricular preload and afterload) control the cardiovascular system to reduce the susceptibility to disturbances that could cause derivations from optimal function. Experiments for study of Cardiovascular Interactions Basic Physiology Change from Normal 1. Arterial Resistance (Vasoconstriction) 200 %. 2. Arterial Resistance (Vasodilation) 50 % 3. Venous Resistance (Venoconstriction) 200 % 4. Venous Compliance 50 % 5. Arterial Compliance 50 % 6. Left Ventricular Contractility 500 % 7. Right Ventricular Contractility 500 % 8. Heart Rate on Stroke Volume and Cardiac Output (Normal, 18, 48, 144, 216 beats/minute) 9 Unstressed blood volume, venous, - 500 ml 10. Venous-return : Cardiac-output relationship. Pathophysiology and Stress 11 Left Heart Failure via Emax 15 % 12. 13. 14. 15. Congestive Left Heart Failure + Blood volume+ 750 ml Congestive Right and Left Heart Failure compared Intrathoracic pressure (Pit) - 4 to 0 mmHg Hemorrhage Blood volume -1750 ml Suggest effective compensatory changes to mimic fluid shifts and reflex control of the cardiovascular system following hemorrhage. 16. Hypertension with arteriosclerosis Ra = 150% and Ca 50 %. Ra is arterial resistance Ca is arterial compliance 17. Exercise Ra = 20 % Explore and describe effective compensatory changes that act to maintain arterial blood pressure while providing a cardiac output of several times normal during vigorous skeletal muscle exercise. 18. Experimental Test Bed. To use the Model without the Tutorial A major revision is underway. A pulmonary venous compartment has been added. The user will be able to develop and use their own parameter set, and separately control right and left ventricular heart rate. CVI Project availability: 1) On a CD from Professor Rothe e-mail: firstname.lastname@example.org 2) As zipped files from the APS Web page http::/advan.physiology.org/cgi/content/full/26/2/98/DC1 Descriptive papers: Rothe, C.F. and Gersting, J.M. “Cardiovascular Interactions: An interactive tutorial and mathematical model.” Advances in Physiology Education 29:98109, 2002. Gersting, J.M. and Rothe. C.F. “Cardiovascular Interactions Tutorial: Architecture and Design.” J. Medical Systems 26:29-38, 2002 Copyright 2002 by Carl F. Rothe Permission is hereby granted to reproduce and distribute copies of this work for nonprofit educational purposes, provided that copies are distributed at or below cost, and that the author, source, and copyright notice are included on or in each copy.